Thermodynamics and Heat Engine4 (3+1)

LESSON - 46 MEASUREMENT OF IP, BP AND HEAT BALANCE CALCULATIONS (NOT INVOLVING COMBUSTION)

Method of determining the mean effective pressure (mep) from the indicator diagram

The actual indicator diagram of 4 stroke petrol engine has been shown in Fig. 46.1. 

Fig. 46.1. Actual indicator diagram of 4 stroke petrol engine.

The mean effective pressure, p_m is calculated from actual indicator diagram by the following equation:

p_m =   x spring scale in bar/cm

       where, p_am is expressed in bar

Net area of indicator diagram (cm²) = Area of power loop – area of pumping loop

                                                              = Net work done /cycle

The area of indicator diagram is measured either by counting squares on graph paper or by use of planimeter.

46.1.1.1.  Indicated Power (IP) for single cylinder engine:

From eqn. (42.1),  Work done/cycle = 100 p_m.V_s=  100 p_m.A . L                        kJ

                                     where,       A  = area of cross-section of piston, m²   ;      L = stroke of engine, m ;

                                                        p_m = mean effective pressure in bars.

  Work done/min. = (Work done/cycle) .(No of cycles per min.)

  Indicated Power of engine =       , kW   

                                              =     , hp

     where, n_c = no. of cycles/min. =  ;         n_mc = no. of missed cycles per min,                        

                 N = speed of the engine, revolutions per min. (rpm),    and  

                 S = number of strokes required to complete one cycle for a particular engine (S = 2 and 4 for 2-strokes and 4 – strokes engines respectively)

   Indicated Power (IP) =        , kW

 46.1.1.2. Indicated Power (ip) for multi cylinder engine:

Indicated Power output (IP) =  , kW

where,  x  = number of cylinder

46.1.2. Brake Power (BP)

It is useful power available at the crank shaft or clutch shaft.  The brake power is less than indicated power because of the following losses as power flows from the cylinder to the crank shaft.

i)     Friction between the cylinder surface and piston rings, in bearings, gears, valve mechanism etc.

ii)    Resistance of air to fly wheel  rotation

iii)   Power required to drive auxiliaries – fuel pump, lubrication pump, radiator circulation pump etc.

Method of measuring brake power (BP) For calculating brake power, toque is measured by coupling a device called dynamometer to the engine output shaft. Dynamometer are of electrical or mechanical type. Further, mechanical dynamometer is either belt or rope brake type. Figure 46.2 shows a rope brake dynamometer. In this dynamometer, two or more ropes of equal lengths are wrapped once round the rim of the wheel, known as brake wheel, fixed on the engine shaft where BP is to be measured. Four or five U-shaped blocks are located at different points of the rim of the wheel so that rope is held in position. A spring balance S to which one end of the rope is attached, is suspended from a beam of a greater height than the wheel E. The other end carries a load W which hangs freely from the wheel. The hanging load W opposes the rotation of the wheel where as the pull S of the spring is in the direction of rotation. Water is supplied to cool the brake drum as the work is converted into friction.

Fig. 46.2. Rope/belt brake dynamometer

The reading is taken at a constant speed of N in r.p.m.

 Let Diameter of the wheel                                     = D                     ,m

       Diameter of the rope                                       = d                      ,m

       Weight of the hanging load                            = W                      ,N

       Spring balance reading                                  = S                      ,N

       Effective circumference of the brake wheel = π (D+d)           ,m

       Effective load                                                   = (W - S)             ,N

       Effective distance of effective load from axis of  rotation = R_eff =              ,m

Torque applied corresponding to effective load, T  = (W-S). R_eff                           , N-m

        Work absorb by the brake per revolution        = (W-S). 2π .R_eff

          = 2π .T

        Revolutions of brake or  revolution of engine shaft  = N          ,r.p.m.

        Brake power (BP)       =       ; kW

46.1.3. Friction Power (FP)

Friction power loss includes loss of power due to sum of all losses (mentioned in above section) which make brake power less than indicated power.

Therefore, Friction Power,  FP = (IP – BP)                                   ; kW

FP increases proportionately with square of speed (N²). For fixed speed i.e. r.p.m. , FP is nearly constant.

46.2. HEAT BALANCE SHEET

Refer Fig. 46.3. Heat energy is supplied to the engine by the combustion of fuel. Out of total heat supplied by the fuel to the engine some part of heat is converted into BP, some part is lost through exhaust gases & cooling water and the remaining part of heat is lost from the engine to the surroundings through frictional and radiative and convective heat losses taken as heat unaccounted. Sheet showing all these energy transactions is called heat balance sheet.

Calculations for these quantities are made in the following way:

Fig. 46.3. Heat balancing of IC engine

Heat supplied by the fuel, Q_fuel

     Q_fuel =  . CV              ; kW  

                where,  (kg/s) is flow rate of fuel into the engine & CV is its calorific value of fuel (kJ/kg).

Heat converted into B.P, Q_BP

Heat converted into Brake power is measured by dynamometer as discussed in lecture 42.

     Q_BP = BP =                       ; kW 

  where   N is speed of the shaft             ; r.p.m.

               T is torque =  (W-S). R_eff           ; N-m

Heat lost through cooling water, Q_w

Heat lost to cooling water is given the following equation

      Q_w = m_w,cyl C_w (T_cyl,_wo – T_cyl,wi)                                    ; kW 

         where  m_w,cy is mass flow rate of water in the jacket of cylinder (kg/s),  

                     C_w is specific heat of water (kJ/kg K),

                     T_cyl,wo & T_cyl,wi are outlet & inlet temperatures of water (K). 

Heat lost through exhaust gases, Q_g

To find heat lost through exhaust gases, these are passed through calorimeter (basically a heat exchanger) as shown in Fig. 46.4 where these gases exchange heat with water.

The heat exchange in the calorimeter is given by

 

            Where, m_w,cal  is mass flow rate of water in the calorimeter (kg/s)

                          C_w is specific heat of water (kJ/kg K),  

                          T_{cal wo} & T_cal,wi are outlet & inlet temperatures of water in calorimeter (K).    

Then heat carried away by exhaust gases is given by the following equation:

Q_g =                      ; kW    

    where, T_go & T_gi are the temperatures of exhaust gases at outlet & inlet of the calorimeter. 

                 T_a is the ambient temperature

Heat unaccounted, Q_unaccounted

Heat lost by friction, radiation and convection

Q_unaccounted = Q_fuel – [Q_BP + Q_w + Q_g ]        ; kW 

Heat balance sheet

Heat balance sheet may be put in tabular form as : —